A probabilistic explanation for the size-effect in crystal plasticity

P. M. Derlet, R. Maaß

Research output: Contribution to journalArticlepeer-review


In this work, the well-known power-law relation between strength and sample size, d-n, is derived from the knowledge that a dislocation network exhibits scale-free behaviour and the extreme value statistical properties of an arbitrary distribution of critical stresses. This approach yields n = (τ + 1)/(α +1), where α reflects the leading order algebraic exponent of the low-stress regime of the critical stress distribution and τ is the scaling exponent for intermittent plastic strain activity. This quite general derivation supports the experimental observation that the size effect paradigm is applicable to a wide range of materials, differing in crystal structure, internal microstructure and external sample geometry.

Original languageEnglish (US)
Pages (from-to)1829-1844
Number of pages16
JournalPhilosophical Magazine
Issue number16-18
StatePublished - Jun 23 2015
Externally publishedYes


  • intermittent flow
  • plasticity
  • sample size effects
  • strength
  • theory

ASJC Scopus subject areas

  • Condensed Matter Physics


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